one rectangle is \framed\ within another. find the area of the shaded region if the \frame\ is 2 units wide.

Answer

Explanation:

Step1: Find outer - rectangle area

The outer - rectangle has length $l = 11$ and width $w = 6$. The area formula for a rectangle is $A = lw$. So, $A_{outer}=11\times6 = 66$.

Step2: Find inner - rectangle dimensions

Since the frame is 2 units wide on each side, the length of the inner - rectangle is $l_{inner}=11-(2 + 2)=7$ and the width of the inner - rectangle is $w_{inner}=6-(2 + 2)=2$.

Step3: Find inner - rectangle area

Using the rectangle area formula $A = lw$, we have $A_{inner}=7\times2=14$.

Step4: Find shaded area

The area of the shaded region is the difference between the area of the outer rectangle and the area of the inner rectangle. So, $A = A_{outer}-A_{inner}=66 - 14=52$.